Joshua Kimmich’s first-half strike had given the champions the lead at BayArena, putting them back on course for the summit heading into the international break.
But a pair of spot-kicks in the second half from Exequiel Palacios instead sealed a deserved comeback for the hosts, who often looked more threatening.
It means Julian Nagelsmann’s side lie second behind Borussia Dortmund heading into the pair’s table-topping Klassiker at the start of April.
Having been leapfrogged by their rivals on Saturday, Bayern knew they needed a result on the road to retake top spot.
After withstanding early Leverkusen pressure, they set about finding it amid torrential rain, with Kimmich drilling a close-range finish home in the 22nd minute, aided by a kind deflection.
For the rest of the first half, however, it was Bayern who appeared to be more on the back foot, Leverkusen creating a flurry of chances, led by Moussa Diaby.
The hosts remained on top following the restart and were rewarded with a penalty after Benjamin Pavard stepped on Amine Adli’s heel.
Palacios converted powerfully to equalise in the 55th minute and stepped up again 18 minutes later when Adli was caught once more by Dayot Upamecano.
The Argentinian again made no mistake to put Leverkusen into a worthy lead, and from there they clung on for a crucial victory that dealt Bayern’s title defence a serious blow.
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